A big chunk of that 15,000 are professionals engaged in research activities (mostly funded by grants and other external funds) e.g. the 1600 folks involved in r

A big chunk of that 15,000 are professionals engaged in research activities (mostly funded by grants and other external funds) e.g. the 1600 folks involved in running the Stanford Linear Accelerator, and activities like fundraising and finances. They mostly are NOT folks 'administering' the faculty in any way. So the comparison with your kid's school is not meaningful. Not to say there are perhaps more administrators than might be ideal. But these numbers aren't helpful in understanding whether that's true. Also, it's worth noting that Stanford is in fact free for folks under the median household income in the U.S. (roughly speaking) which seems pretty 'affordable'. Of course the economics of one of these large-endowment, research intensive institutions is pretty much unrelated to their teaching function. But that just highlights the weakness of using gross, whole-institution numbers of people/dollars for any sort of comparison. Big universities serve lots of ends (not just teaching undergrads) and so the teasing apart the economic picture (and whether it's efficient at meeting it's many goals) is complicated.